Question 2
Find all $f:(0,\infty)\to(0,\infty)$ such that
$$f(x+1/y)+f(y+1/z)+f(z+1/x)=1$$
for all $x,y,z\gt 0$ with $xyz=1$.
Proposed by Titu Andreescu, Nikolai Nikolov. Source: Evan Chen’s third-party compilation, not an official publication. One editorial point; manual grading only.
$$f(x+1/y)+f(y+1/z)+f(z+1/x)=1$$
for all $x,y,z\gt 0$ with $xyz=1$.
Proposed by Titu Andreescu, Nikolai Nikolov. Source: Evan Chen’s third-party compilation, not an official publication. One editorial point; manual grading only.